Third party payer health systems can never work as effectively as a true free market approach. Government can't manage anything efficiently, since the profit motive is missing. Insurance companies like the current system that excludes competition.
In my book, "Fixing Everything", I describe a new form of healthcare called "Group Self Insurance". Members retain ownership of their monthly contributions. The group pools these contributions to cover catastrophic medical problems. At the end of each month costs for the month are applied against the individual's contribution, including: a small administrative fee, personal medical costs, and shared catastrophic costs. The remaining amount is applied against the next month's contribution.